The control-coding (CC) capacity of dynamical decision models (DMs) is defined as the maximum amount of information transfer per unit time from its inputs to its outputs, called CC rate R in bits/second, which is operational with the aid of a controller-encoder and a decoder, as in Shannon's mathematical theory of communication over noisy channels, with the encoder replaced by a controller-encoder [C. Kourtellaris and C. D. Charalambous, IEEE Trans. Inform. Theory, 64 (2018), pp. 4962-4992]. In the first part of the paper, data processing inequalities and information structures of optimal controllers-encoders are derived for controlled and uncontrolled information processes. Further, the ergodic theory of a Markov decision is applied to establish direct and converse CC theorems. In the second part of the paper, the problem of signalling information via a Gaussian decision model (G-DM) subject to a quadratic cost constraint to another Gaussian control system (G-CS) with a quadratic pay-off is investigated. A hierarchical decomposition and decentralized optimality of linear quadruple of strategies, {controller-encoder, decoder, controller}, is shown by construction as follows: (i) the controller-encoder simultaneously controls the output of the G-DM and encodes the state of the G-CS, and operates at the CC capacity of the G-DM; (ii) the decoder is optimal with respect to a mean square error (MSE) criterion; and (iii) the controller of the G-CS which acts on the decoder's information is optimal.